Technology E: Input Coordinates (10, 1) and Coal-to-Labor Ratio

Cost Minimization in Production

A textile firm has two available methods for producing 100 meters of cloth. Both methods require inputs in a fixed ratio, and the cost per meter remains the same regardless of the total quantity produced.

• Method A requires 5 workers and 2 tons of coal.
• Method B requires 2 workers and 6 tons of coal.

If the daily wage for a worker is $40 and the price of coal is $10 per ton, which method should the firm choose to minimize its production costs?

Applicability of a Simplified Production Model

Production Inefficiency with Input Changes

Production Inefficiency with Input Changes

A manufacturing process requires a strict input ratio of 2 workers for every 1 machine. A firm using this process observes that doubling the number of workers and machines results in a 150% increase in total output. Based on this information, is it true that this production technology exhibits both fixed proportions and constant returns to scale?

Adapting Production to Changing Input Costs

A company manufactures a product using a technology that requires a fixed ratio of inputs and exhibits constant returns to scale, meaning the cost per unit does not change with the production volume. The company has two production methods available:

• Method X: Uses a large amount of labor and a small amount of machinery.
• Method Y: Uses a small amount of labor and a large amount of machinery.

Currently, the company uses Method X. If a new regulation causes the cost of labor to increase significantly while the cost of machinery stays the same, which of the following outcomes is the most likely long-term response for the company?

Analyzing Production Technology Characteristics

A simplified economic model of a firm's production process is built on two key assumptions about its technology. Match each assumption with its direct implication for the firm's operations.